Thermal Characterization and Predictive Modeling of Thermo-Elastic Errors in Five-Axis Machining Centers Using Dynamic R-Test

Five-axis machining centers are essential for manufacturing complex, high-precision parts. However, their accuracy is significantly affected by thermally induced geometric errors, also known as thermo-elastic errors. This paper presents a comprehensive approach to thermal characterization and its potential application in predictive modeling on a five-axis machine tool demonstrator, showcasing the capabilities of a novel dynamic R-test measurement method. Based on a previously developed and validated dynamic R-test measurement method that enables the rapid, volumetric acquisition of machine deviations during continuous movement, detailed experimental investigations were conducted under various single- and combined-axis loading scenarios. The extensive dataset and detailed error information provided by the dynamic R-test method enabled thorough analysis and correlation of thermo-elastic errors, including translational and rotational errors, with temperature and control-internal axis data. A well-established phenomenological model based on PT1 transfer functions is used, detailing its input variables and parameter determination methods. The model’s predictive capability was rigorously validated against independent datasets, demonstrating significant reductions in primary errors (up to 70% in maximum residual and 80% in RMSE). This study identifies the most influential error types and their correlation with thermal loads. This confirms the feasibility of robustly predicting thermo-elastic behavior and enhancing the volumetric accuracy of five-axis machine tools, particularly by leveraging the detailed error insights enabled by the dynamic R-test.